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Master equations and simulation algorithms for the discrete‐stochastic approach

Daniel T. Gillespie and Effrosyni Seitaridou

in Simple Brownian Diffusion: An Introduction to the Standard Theoretical Models

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199664504
eISBN:
9780191748516
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199664504.003.0006
Subject:
Physics, Soft Matter / Biological Physics

The discrete-stochastic model of diffusion introduced in the preceding chapter implies that the system state evolves in time as what is known as a jump Markov process. The time evolution of such a ... More


Numerical Simulation for Biochemical Kinetics

Daniel T. Gillespie and Linda R. Petzold

in System Modeling in Cellular Biology: From Concepts to Nuts and Bolts

Published in print:
2006
Published Online:
August 2013
ISBN:
9780262195485
eISBN:
9780262257060
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262195485.003.0016
Subject:
Mathematics, Mathematical Biology

This chapter discusses concepts and techniques for mathematically describing and numerically simulating chemical systems that into account discreteness and stochasticity. The chapter is organized as ... More


Computing Chemical Reactions

Wolfgang Banzhaf and Lidia Yamamoto

in Artificial Chemistries

Published in print:
2015
Published Online:
September 2016
ISBN:
9780262029438
eISBN:
9780262329460
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262029438.003.0004
Subject:
Public Health and Epidemiology, Public Health

This chapter examines various reactor algorithms that are frequently used in artificial chemistries. We contrast macroscopic, deterministic reaction algorithms and microscopic, stochastic reaction ... More


Utility Evaluation of Risk in Retirement Saving Accounts

James M. Poterba, Joshua Rauh, Steven F. Venti, and David A. Wise (eds)

in Analyses in the Economics of Aging

Published in print:
2005
Published Online:
February 2013
ISBN:
9780226902869
eISBN:
9780226903217
Item type:
chapter
Publisher:
University of Chicago Press
DOI:
10.7208/chicago/9780226903217.003.0002
Subject:
Economics and Finance, Econometrics

This chapter evaluates the effect of holding a broadly diversified portfolio of common stocks compared to a portfolio of index bonds on the distribution of 401(k) account balances at retirement using ... More


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